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Math Challenge #3 [HIJACKED] *** SOLVED!!

TuxDave

TuxDave

Lifer
Was a little impatient and wanted to see the talent of ATOT. 🙂 I stole this from someone a while ago.

100 pirates come upon 5050 coins. To divide it up, they write the numbers 1 through 100 on paper and toss it in a hat. Each pirate then draws a number and holds onto it. The number represents the number of coins they'll get. Assuming they all play to win the most amount of money (without cheating/killing/etc....), what is the best strategy for a pirate to have?

OOPS.. just wait one sec...

Add to above: All pirates that don't like their number can toss it in the hat and draw new ones from the new pile. All pirates that like it, can keep it and don't have to redraw.
 
On the first draw, if they get 50 or higher, keep it.
On the next draw, if they get 25 or higher, keep it.
On the third draw, if they get 13 or higher, keep it.
On the fourth draw, if they get 7 or higher, keep it.
On the fifth draw, if they get 4 or higher, keep it.
On the sixth draw, if they get 2 or higher, keep it.
 
Originally posted by: marquee
On the first draw, if they get 50 or higher, keep it.
On the next draw, if they get 25 or higher, keep it.
On the third draw, if they get 13 or higher, keep it.
On the fourth draw, if they get 7 or higher, keep it.
On the fifth draw, if they get 4 or higher, keep it.
On the sixth draw, if they get 2 or higher, keep it.
Click to expand...

Nope! *rereads my question carefully if I didn't screw it up*
 
HARRRRRRRRRR!

Aye matey, don't make me drop my gangplank to ye poop deck and send my seamen to plunder ye booty!
 
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
 
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

but if the first one gets 1? he can redraw.
 
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

Are the pirates cognizant of what the others draw? He didn't say that, and you can't assume that because they didn't redraw that they drew the highest possible.
 
Originally posted by: Amorphus
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

but if the first one gets 1? he can redraw.
Click to expand...

We have a winnar!!! Oh... the person with the 1 is just plain screwed....
 
Originally posted by: Amorphus
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

but if the first one gets 1? he can redraw.
Click to expand...

he's looking for the best strategy right? so why waste time redrawing, he could be out plundering more loot!
 
Originally posted by: Descartes
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

Are the pirates cognizant of what the others draw? He didn't say that, and you can't assume that because they didn't redraw that they drew the highest possible.
Click to expand...

Oh... did I mess up? I meant to include that the redraw happens after everyone picked out a number. THEN all unhappy people toss it in and only they play again.
 
Originally posted by: TuxDave
Originally posted by: Descartes
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

Are the pirates cognizant of what the others draw? He didn't say that, and you can't assume that because they didn't redraw that they drew the highest possible.
Click to expand...

Oh... did I mess up? I meant to include that the redraw happens after everyone picked out a number. THEN all unhappy people toss it in and only they play again.
Click to expand...

Yeah, that would have been helpful, at least for me 🙂
 
Originally posted by: Descartes
Originally posted by: TuxDave
Originally posted by: Descartes
Originally posted by: marquee
Ok, attempt #2.

pirate with 100 wont redraw, since he's got the highest already.
pirate with 99 wont redraw either, since he knows 100 wont redraw, and he has no chance to improve.
pirate with 98 then wont redraw, since both 100 and 99 wont redraw.
etc etc..

so there are never any redraws!

GAMEOVER
Click to expand...

Are the pirates cognizant of what the others draw? He didn't say that, and you can't assume that because they didn't redraw that they drew the highest possible.
Click to expand...

Oh... did I mess up? I meant to include that the redraw happens after everyone picked out a number. THEN all unhappy people toss it in and only they play again.
Click to expand...

Yeah, that would have been helpful, at least for me 🙂
Click to expand...

lol.. my bad. English isn't my strong point.
 
This isn't a math problem.. it's a problem about guessing how smart your opponents are.

Regardless of strategy, the average pirate get's 50.5 gold pieces. No matter what strategy they use. Thus, overall, the number of people who improve their status will be equal to the number of people who go down. If only the people with number 1-50 were throwing back their numbers, then anyone above 25 would stand a greater chance of going down than going up (obviously not a good strategy for them!!) So, we can safely assume it's stupid to throw your number back if you have above 25. But, if the pirates are smart enough to follow that strategy (making them smarter than marquee), then we can safely assume that anyone throwing back a 13 or higher has a greater chance of losing than winning.... and so on.

So, the only decent strategy would be to hold on to whatever you get. The only pirate throwing his number in is the one with 1. A 2nd part of the good strategy would be to keep your mouth shut and not say "sucks to be you!" to the pirate with only 1. Because we all know pirates carry swords and seem to be pretty short tempered.

edit: it took me too long to type that!

BTW, it doesn't matter that the OP didn't state that everyone picks before there's any redrawing.
If anyone could redraw, it'd clearly only suck for the last person drawing, since he'd be stuck with 1.
(1st person drawing gets a 98... redraws... redraws... redraws... redraws... redraws... until he gets 100)
If the person doesn't know his position, the 2nd person would redraw, redraw, redraw, ad infinitum, hoping to eventually get a 100... and after 45 minutes might tire and stick with the 99. The the 3rd person would eventually settle for 98... etc. until a week or so later they get down to the 100th person.
 
Originally posted by: DrPizza
This isn't a math problem.. it's a problem about guessing how smart your opponents are.

Regardless of strategy, the average pirate get's 50.5 gold pieces. No matter what strategy they use. Thus, overall, the number of people who improve their status will be equal to the number of people who go down. If only the people with number 1-50 were throwing back their numbers, then anyone above 25 would stand a greater chance of going down than going up (obviously not a good strategy for them!!) So, we can safely assume it's stupid to throw your number back if you have above 25. But, if the pirates are smart enough to follow that strategy (making them smarter than marquee), then we can safely assume that anyone throwing back a 13 or higher has a greater chance of losing than winning.... and so on.

So, the only decent strategy would be to hold on to whatever you get. The only pirate throwing his number in is the one with 1. A 2nd part of the good strategy would be to keep your mouth shut and not say "sucks to be you!" to the pirate with only 1. Because we all know pirates carry swords and seem to be pretty short tempered.
Click to expand...

hmm, i wonder if people read all the posts in the thread before they answer.
 
Originally posted by: DrPizza
This isn't a math problem.. it's a problem about guessing how smart your opponents are.

Regardless of strategy, the average pirate get's 50.5 gold pieces. No matter what strategy they use. Thus, overall, the number of people who improve their status will be equal to the number of people who go down. If only the people with number 1-50 were throwing back their numbers, then anyone above 25 would stand a greater chance of going down than going up (obviously not a good strategy for them!!) So, we can safely assume it's stupid to throw your number back if you have above 25. But, if the pirates are smart enough to follow that strategy (making them smarter than marquee), then we can safely assume that anyone throwing back a 13 or higher has a greater chance of losing than winning.... and so on.

So, the only decent strategy would be to hold on to whatever you get. The only pirate throwing his number in is the one with 1. A 2nd part of the good strategy would be to keep your mouth shut and not say "sucks to be you!" to the pirate with only 1. Because we all know pirates carry swords and seem to be pretty short tempered.

edit: it took me too long to type that!

BTW, it doesn't matter that the OP didn't state that everyone picks before there's any redrawing.
If anyone could redraw, it'd clearly only suck for the last person drawing, since he'd be stuck with 1.
(1st person drawing gets a 98... redraws... redraws... redraws... redraws... redraws... until he gets 100)
If the person doesn't know his position, the 2nd person would redraw, redraw, redraw, ad infinitum, hoping to eventually get a 100... and after 45 minutes might tire and stick with the 99. The the 3rd person would eventually settle for 98... etc. until a week or so later they get down to the 100th person.
Click to expand...

Yeah... my mistake. I added in one more crucial line somewhere down the post.
 
Originally posted by: fivespeed5
HARRRRRRRRRR!

Aye matey, don't make me drop my gangplank to ye poop deck and send my seamen to plunder ye booty!
Click to expand...


damn. that's some pent-up homosexual rage that you have there. poop deck...seamen...plundering booty. :Q
 
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